After a theoretical analysis of system singularities, and normalized equations describing the water-level motion in the throttled surge tank of a hydropower plant are solved on a digital computer. The critical stability conditions for large amplitude oscillations are obtained by finding the conditions under which the initial state point of the system is, in the terminology of the phase plane method, on the limit cycle. The paper demonstrates the possibility of the existence of 2 limit cycles around the singularity representing the steady operating point and the feasibility of the adoption of surge tanks with a section smaller than Thoma critical value.